Design of a Preview Controller for Discrete-Time Systems Based on LMI

Abstract

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

“…Therefore, it is obvious that if one can design a guaranteed cost static output feedback controller (33) to robustly stabilize the augmented system (27), then the preview repetitive controller (7) can also stabilize the original system (1) and such that lim k→∞ e(k) = 0.…”

“…In the following, we will give the sufficient conditions for the existence of a guaranteed cost static output feedback controller (33) to robustly stabilize the augmented system (27).…”

“…Clearly, a conventional feedback control system does not take full advantage of the known future values, i.e., M r = 0 and M d = 0. Hypothes A2 indicates that the reference signal and the disturbance signals have impacted performance of the control system significantly only for a certain time period[17,32,33].…”

Parameter‐dependent preview control with robust tracking performance

“…The future values of the reference signal are assumed not to change beyond the , namely, Remark 2 A2 is the assumption that the reference signal is previewable. Theoretical research and practical examples have shown that the previewable signal has impacted performance of the control system significantly only for a certain time period, during which the reference signal exceeds the preview length impact is small; therefore, the reference signal is assumed to be some constant when it exceeds the preview length [37]. In fact, a regular feedback control system does not take full advantage of the known future values, or equivalently, .…”

H∞ Preview Control of A Class of Uncertain Discrete‐Time Systems

“…In order to reflect the uncertainty, the uncertain parameters a i ( i = 1 , 2 , 3 , 4 , 5), with absolute values no more than 0.5, are taken as random numbers. Note that if the selecting method for the auxiliary variables and in is adopted, then the initial conditions should be decided based on different situations. The proposed method can avoid the limitation on initial conditions.…”